The activity of a radioactive material is 2.56 × 10–3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 × 10–5 Ci

To solve this problem, we can use the formula for radioactive decay:

A = A₀ * (1/2)^(t / T)

Where: A is the final activity A₀ is the initial activity t is the time elapsed T is the half-life of the material

We are given that the initial activity (A₀) is 2.56 × 10–3 Ci and the final activity (A) is 2 × 10–5 Ci. We need to find the time elapsed (t).

Let's substitute the given values into the formula:

2 × 10–5 = 2.56 × 10–3 * (1/2)^(t / 5)

Now, let's solve for t. First, divide both sides of the equation by 2.56 × 10–3:

(2 × 10–5) / (2.56 × 10–3) = (1/2)^(t / 5)

Next, take the logarithm of both sides of the equation to solve for t:

log[(2 × 10–5) / (2.56 × 10–3)] = log[(1/2)^(t / 5)]

Using logarithm properties, we can bring down the exponent:

log[(2 × 10–5) / (2.56 × 10–3)] = (t / 5) * log(1/2)

Now, divide both sides of the equation by log(1/2):

[t / 5] = log[(2 × 10–5) / (2.56 × 10–3)] / log(1/2)

Finally, multiply both sides of the equation by 5 to solve for t:

t = 5 * [log[(2 × 10–5) / (2.56 × 10–3)] / log(1/2)]

Using a calculator, we can evaluate the right side of the equation to find the value of t.